Regression Data Analysis

Garant předmětu:

Jiří Franc, Tomáš Hobza

Lecturer:

Tomáš Hobza

Tutor:

Jiří Franc, Tomáš Hobza

Supervisor:

Department of Mathematics

Synopsis:

1.Simple linear regression: least squares estimation, properties of parameter estimates, hypotheses tests and confi-dence intervals for parameters of the model, model-based prediction, analysis of residuals

2.Multiple linear regression: general linear model, least squares estimation, analytical and numerical solutions of the normal equations, properties of parameter estimates, coefficient of determination, F-test, prediction intervals

3.Residuals, diagnostics and transformations: residuals and residual plots, normality tests, detection of outlying and influential observations, hat matrix, Cook’s distance, transformations of dependent and independent varia-ble, Box-Cox transformation

4.Selection of a regression model: criteria functions, R2 statistics, Mallows’ Cp statistics, Akaike and Bayes infor-mation criteria, stepwise regression and backward elimination

5.Multicollinearity: impact of multicollinearity on precision of the parameter estimates, detecting and combatting multicollinearity, ridge regression

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] Golberg, M. Cho, H.A.: Introduction to Regression Analysis. WITpress, Southampton 2010.

[2] Olive, D.: Linear Regression. Springer, 2017.

Recommended references:

[3] Weisberg, S.: Applied Linear Regression. John Wiley & Sons, New Jersey 2014.

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

• Aplikované matematicko-stochastické metody (compulsory course in the program)